Nanoscale Polar Heterogeneities and Branching Bi-Displacement Directions in K_0.5Bi_0.5TiO₃

K0.5Bi0.5TiO3 (KBT)—one of the few perovskite-like ferroelectric compounds with room-temperature tetragonal symmetry—differs from other members of its family (BaTiO3 and PbTiO3) by the presence of a disordered mixture of K and Bi on cuboctahedral sites. This disorder is expected to affect local atomic displacements and their response to an applied electric field. We have derived nanoscale atomistic models of KBT by refining atomic coordinates to simultaneously fit neutron/X-ray total scattering and extended X-ray absorption fine-structure data. Both Bi and Ti ions were found to be offset relative to their respective oxygen cages in the high-temperature cubic phase; in contrast, the coordination environment of K remained relatively undistorted. In the cubic structure, Bi displacements prefer the ⟨100⟩ directions and the probability density distribution of Bi features six well-separated sites; a similar preference exists for the much smaller Ti displacements, although the split sites for Ti could not be resolved. The cation displacements are correlated, yielding polar nanoregions, whereas on average, the structure appears as cubic. The cubic ↔ tetragonal phase transition involves both order/disorder and displacive mechanisms. A qualitative change in the form of the Bi probability density distribution occurs in the tetragonal phase on cooling to room temperature because Bi displacements “branch off” to ⟨111⟩ directions. This change, which preserves the average symmetry, is accompanied by the development of nanoscale polar heterogeneities that exhibit significant deviations of their polarization vectors from the average polar axis.